Smooth orthogonal drawings of planar graphs

Muhammad Jawaherul Alam, Michael A. Bekos, Michael Kaufmann, Philipp Kindermann, Stephen G. Kobourov, Alexander Wolff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

In smooth orthogonal layouts of planar graphs, every edge is an alternating sequence of axis-aligned segments and circular arcs with common axis-aligned tangents. In this paper, we study the problem of finding smooth orthogonal layouts of low edge complexity, that is, with few segments per edge. We say that a graph has smooth complexity k - for short, an SC k -layout - if it admits a smooth orthogonal drawing of edge complexity at most k. Our main result is that every 4-planar graph has an SC2-layout. While our drawings may have super-polynomial area, we show that for 3-planar graphs, cubic area suffices. We also show that any biconnected 4-outerplane graph has an SC1-layout. On the negative side, we demonstrate an infinite family of biconnected 4-planar graphs that require exponential area for an SC 1-layout. Finally, we present an infinite family of biconnected 4-planar graphs that do not admit an SC1-layout.

Original languageEnglish (US)
Title of host publicationLATIN 2014
Subtitle of host publicationTheoretical Informatics - 11th Latin American Symposium, Proceedings
PublisherSpringer-Verlag
Pages144-155
Number of pages12
ISBN (Print)9783642544224
DOIs
StatePublished - Jan 1 2014
Event11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay
Duration: Mar 31 2014Apr 4 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8392 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th Latin American Theoretical Informatics Symposium, LATIN 2014
CountryUruguay
CityMontevideo
Period3/31/144/4/14

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Alam, M. J., Bekos, M. A., Kaufmann, M., Kindermann, P., Kobourov, S. G., & Wolff, A. (2014). Smooth orthogonal drawings of planar graphs. In LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings (pp. 144-155). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-642-54423-1_13